It is clear that if the mass of Ice placed in a given mass of water comes out greater accord- 

 ing to formula (3), then, as a result of interaction of water and ice, accretion occurs, but if less, 

 melting of ice occurs. 



If we examine the extreme possible case in the coexistence of water and ice, namely, that 

 the ice placed in water melts completely, i.e. , N =n, then we obtain from formula (2) 



N = Mc^ ■ , ^^~' , . (4) 



It is natural that the limit of the mass of ice which can be melted by a given mass of water is 

 governed by the condition that by the end of the process the temperature of the water decreases to 

 the freezing temperature and therefore the entire reserve of heat found in the water is used up. 



The following formulas serve in saline interactions: 



MS^ + nS,=^(M+n)S, (5) 



where Syj is the initial salinity of sea water, 



Sj is the salinity of the ice, 



S is the final salinity of the water. 



From formula (5) we obtained 



It is clear that if the final salinity of the water is lower than the initial salinity (under the 

 condition that the salinity of the ice is less than the water), then melting occurs, and if it is 

 greater — freezing occurs. 



There is some interest in treating more completely the factors which condition the coexist- 

 ence of water and ice without changes in their masses. It is not difficult to see that coexistence 

 can occur only under the following conditions: 



1. The temperature of the water and ice are the same and equal to the freezing temperature 

 of the water in which the ice floats. From this condition it follows that 



But the freezing temperature and the salinity of sea water, as we have seen in Section 5, are 

 related by the formula 



T = -0.054 So,. 



Inasmuch as in the investigated case there are no reasons which cause melting or freezing, 

 there are also no reasons for changing the initial salinity of sea water, i.e. , we should have the 

 equation <^ t^ 



The investigated case is an example of thermic (due to the equality of temperature, there is 

 no heat exchange between water and ice) and dynamic (no change in the mass of the water and ice) 

 equilibrium. 



156 



